Energetically-optimized

The first step in the DG calculations is the generation of the holonomic distance matrix for aU pairwise atom distances of a molecule [121]. Holonomic constraints are expressed in terms of equations which restrict the atom coordinates of a molecule. For example, hydrogen atoms bound to neighboring carbon atoms have a maximum distance of 3.1 A. As a result, parts of the coordinates become interdependent and the degrees of freedom of the molecular system are confined. The acquisition of these distance restraints is based on the topology of a model structure with an arbitrary, but energetically optimized conformation. 

Figure 2.26 Energetic optimization, i.e., "minimal stress" for co-rotating and counter-rotating screws...

Energetical optimization of supercritical fluid extraction processes U. Sievers... 

We proceed as in section 4, where it was shown that because the mean aggregation number N is close to the (energetically) optimal aggregation number M, the area per lipid is also close to Oq the consequent error in assuming o = Uq is not large. 

Certain substituted urea compounds, such as phenylurea or thidiazuron. Fig. (1), are very effective in the replacement of adenine-based cytokinins in promoting callus growth and other bioassays [27,28]. Molecular modeling revealed that the energetically optimal conformation of active urea derivatives have similar geometry as the isoprenoid side chain, so they can bind to the active sites of cytokinin metabolic enzymes and/or activate cytokinin receptors [29]. Thus, these compounds are likely to enhance their cytokinin effect by simultaneous activation of the receptor and inhibition of some of the cytokinin deactivating enzymes [11,30]. 

In order to clarify differences in bond nature between the AM and AE tetramers, we examined the electronic structures of U4, Na4, K4, 864, Mg4, and Ca4 tetramers. We found the energetically optimal structures for the tetramers using ADF. The rhombus geometry is stable for the AM tetramers, while the tetrahedral one is stable for the AE tetramers. 

Recently, van Eijck and Kroon discussed the implications of dependence of the electrostatic energy of a crystal on its macroscopic shape if the crystal has a nonzero dipole moment. Ewald summation then results in the lowest possible energy. This minimum energy corresponds to the situation that the crystal finds an energetically optimal shape (a needle, with the dipole moment directed along the needle axis, or a platelet with the dipole moment in its plane) and/or... 

Fig. 7.24 Energetically optimized structures of phenol with one, three, and five ammonia molecules in the ground state. (Reprinted with permission from K. Nagashima et al., J. Phys. Chem. A 116, 11167 (2012)).

The hydrolysis step is more controversial, but one view (Roberts et al., 1969) is that it occurs by a reversal of the sequences followed during cyclization. Recently, Cozzone and Jardetzky (1977) studied the interaction of the single-stranded synthetic polynucleotide, poly(A), in the presence of RNase. They found that the enzyme can carry out the cyclization step on such polypurine nucleotides, but not the hydrolysis step. They interpreted their data to indicate that this nonoptimal substrate forms an enzyme-substrate complex which allows alignment with only one of the two active-site histidines. This emphasizes two important points for the mechanism of pancreatic RNase and other enzymes (1) binding must be correct to have the energetically optimal interaction with the enzyme that will lead to the formation of the transition state ... 

The techniques for solving the Kohn-Sham equation are similar to those used for the Hartree-Fock equation. Commonly, the orbitals are expanded in basis functions, and a secular equation is solved to find the energetically optimal coefficients of the expansion. The literature on suitable basis sets is enormous and cannot be reviewed here. It is common practice to use in DFT calculations the same basis sets developed for Flartree-Fock and Cl calculations, although it is not always clear (in particular in the case of correlation-consistent bases) if this is always an optimal choice. 

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